Translation Matrix Coordinates
I expect part of the issue comes from you having the camera still following the curve after you have keyframed it. Remove the follow path constraint from the camera after you have the locations for the keyframes.

For your code - don't change frame_current, you should use frame_set(), but in your example you don't need to use either as you are specifying the frame when you create the keyframe.

I would use something like -

import bpy

# each item is time_offset, x, y, z
verts = [
    [0.0, -0.0017,   -6.6515,  5.0],
    [0.1, 58.6404,  -36.0573,  3.0],
    [0.2, 15.9993,  -53.7007,  3.0],
    [0.3, 58.6404,  -71.3442,  7.0],
    [0.4, 15.9993,  -88.9876, 10.0],
    [0.5, 58.6404, -106.6311,  5.0],
    [0.6, 15.9993, -124.2746,  6.0],
    [0.7, 58.6404, -141.9180,  7.0],
    [0.8, 26.6595, -159.5615,  8.0],
    [0.9, 79.9609, -165.4426,  9.0],
]

camera_object = bpy.data.objects['Camera']

for point in range(len(verts)):
    cur_frame = 2160 * verts[point][0]
    camera_object.location = (verts[point][1],verts[point][2],verts[point][3])
    camera_object.keyframe_insert(data_path="location", frame=cur_frame)